Geomechanical modeling seeks to accurately calculate the displacements, stresses and strains within an earth volume of interest, given certain elastic boundary conditions and a distribution of body forces. Similarly, the newer and closely related discipline of digital rock physics seeks to accurately calculate the elastic stiffness of a 3D gridded representation of a rock sample. In both applications it is necessary to calculate the solution of a well-defined elastostatic boundary value problem in a heterogeneous elastic model, requiring considerable computational effort.
Current solution methods rely predominantly on the Finite Element Method (FEM) to solve this equation for the output of interest. FEM is an accurate solution method, but it suffers on two counts: it requires that one build a sophisticated FEM mesh via a laborious workflow, and the large resulting stiffness matrix requires a non-trivial matrix solver algorithm, both of which impede the workflow.
There is a need for earth modeling methods that can accurately estimate stresses, strains, and stiffness in the presence of extreme heterogeneity. Such earth models can be used to guide decisions in acquisition, processing, imaging, inversion, and hydrocarbon reservoir property inference, as well as estimating locations of potential geomechanical drilling hazards, and ultimately impacting decisions on geomechanically lower risk and geologically optimum well placement, so improving hydrocarbon recovery.